GNU Scientific Library Reference Manual - Revised Second Edition (v1.8) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi Paperback (6"x9"), 636 pages, 60 figures ISBN 0954161734 RRP £24.99 ($39.99) Get a printed copy>>>

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7.6 Clausen Functions

The Clausen function is defined by the following integral,

Cl_2(x) = - \int_0^x dt \log(2 \sin(t/2))

It is related to the dilogarithm by Cl_2(\theta) = \Im Li_2(\exp(i\theta)). The Clausen functions are declared in the header file ‘gsl_sf_clausen.h’.

Function: double gsl_sf_clausen (double x)

Function: int gsl_sf_clausen_e (double x, gsl_sf_result * result)

These routines compute the Clausen integral Cl_2(x).